Originally Posted by
DELLAS
Hmm well youve convinced me , I will try my luck with maybe doing MIA-LAX Via ORD then overnight in LA and then fly LAX-LHR the next day. I might get away with it

If they won't let you do that, how about trying singles LHR-FRA-MIA(stop)-xxx-LAX and then LAX-LHR. The outbound is a push, but it's not backtracking, and if it works you get to try NZ oneway.
Or LHR-FRA-MIA-DEN and DEN-LAX-LHR which has a less complicated outbound, but some less-major backtracking.